Triple Draw with a Twist: What’s an Extra Card Worth?
Last Friday, I saw Daniel Negreanu mention on Twitter that he was playing a 2-7 Triple Draw cash game with a twist that was apparently new to him. Based on some of the responses, it seems that it’s an idea that’s not unique to the game he was playing in, but not all that common either; some of his fellow professionals had seen it before or even said they play the variant in question regularly, while others had not. Conceptually, it’s a simple gimmick: the game is played according to all the normal rules, except that the player under the gun has the option to post a straddle (that is, to make a blind raise to two big blinds) in return for the privilege of being dealt a sixth card in the first round. The player will still only get to draw back to five cards during subsequent draw phases, so the practical effect is simply to improve the player’s chances of getting a good starting hand, after which they will be on equal footing with the opponents. In a way, it’s comparable to the Pineapple variant of Texas Hold’em.
Those who’ve never played Triple Draw variants are recommended to read my article on the subject for the Dealer’s Choice series, but the nutshell version is this: Everyone normally gets five cards each. There are then four betting rounds (almost always Fixed Limit, the first two with small bets, the latter two with big bets). In between betting rounds, players still in the hand can exchange any number of cards or stand pat. The lowest hand at showdown wins the pot; pairs always count against you, and in 2-7, so do straights and flushes (unlike in the less popular A-5 variant).
Playing 2-7 triple draw with a fun wrinkle: if you straddle the big blind you start with an extra card! I will be exercising that option.
— Daniel Negreanu (@RealKidPoker) March 18, 2016
Mixing up the mixed games
So-called “mixed games” (that is, anything that isn’t Hold’em or Omaha) are very popular in the world of high stakes cash games. In part, this is simply to break up the monotony, since cash games lack the narrative and progression that tournaments provide, so playing long sessions of Hold’em every single day would quickly get old. More importantly, though, the amount of information available for the flop-based games is enormous thanks to their popularity; when playing for serious stakes, then, it’s hard to find truly clueless recreational players, and hard to have a huge edge over tight, reasonably knowledgeable opponents. Mixed games, then, provide an opportunity for pros to play games with which they have experience, but with which their opponents are hopefully not quite so comfortable.
Now, though, even the “standard” mixed games like Triple Draw are starting to feel stale, so one often hears about various novel ideas being tried out. Sometimes, these are pretty fundamental alterations to the game’s basic nature and strategy, as in the case of Duck Flush. Other times, they’re essentially mash-ups of two existing games, such as Baducy, a split pot game in which half the pot is awarded to the best 2-7 Triple Draw hand, and the other half to the best Badugi hand. Finally, there are smaller adjustments, like the one we’re discussing. Regardless of how extreme the changes are, though, the fundamental goal is usually the same: to create incentives and temptations for players to play more and bigger pots, and add additional opportunities for weaker players to make costly mistakes.
But who are the fish: those who take the extra card or those who don’t?
It’s clear how this twist – which I’ll call Straddle-Six for lack of a better name – stimulates additional action. Players who invoke the rule are committing themselves to playing nearly any hand they’re dealt, due to the extra money invested, and will usually be forced to call at least one additional raise. Meanwhile, having three blinds serves roughly the same function as antes, increasing the amount of money in the pot to start the hand, and encouraging players to enter the hand with more marginal holdings as a result.
What’s less clear is who is actually making a mistake: those who choose to straddle for the extra card, or those who decline. Several other experienced pros got into a Twitter debate over it, some of whom felt that it’s a slam-dunk decision to do it, others who felt that it would be a loss-making decision in the long run. Negreanu’s opinion was that it’s a good idea in four-handed play, close to break-even when you add a fifth player, and a losing proposition with six or more, which may well be correct. Certainly, there are good reasons that it becomes either a better decision or a less bad one the fewer players there are, which we’ll get to in a moment. First, though, let’s try to quantify exactly what benefit you get by taking the extra card, and what it’s really costing you.
— David Baker (@audavidb) March 18, 2016
The tangible benefit
The direct benefit of the extra card is fairly obvious: some percentage of the time, you’ll start with a slightly or significantly stronger hand than you would have had otherwise. How much stronger? Well, I took a look at some of the probabilities involved in the game to see how much more often certain desirable combinations come up.
As the name of the game would suggest, the best starting hands in 2-7 – the sort you’d be likely to play under the gun voluntarily – all include both a Deuce and a Seven, since those two cards are both required in order to make the nuts or the near nuts; the best category of hands you can make are Seven High, and to manage this without making a straight, you need the Deuce as well. Conversely, cards in the Three to Six range are all desirable, but you only need three of the four, so none of them are must-haves.
Ordinarily, your odds of getting one or the other (the Deuce being more important) are around 34%, while adding a sixth card boosts you up to 40%. The impact is greater when it comes to getting both, however. There, you’re only 10% with five cards, and 14% with six, so that’s a significant improvement, proportionally speaking. Of course, once you have those two cards, you’re pretty likely to have one of the fill cards as well – 70% with five cards and 80% with six – so it’s probably okay to assume that when we have them, we’re on a two-card draw or better.
Given that you have a Seven, a Deuce and at least one fill card, then your odds of being on a one-card draw (or pat Seven if you’re really lucky) are about 44%, while they’re more like 67% with the sixth card. So here too, the percentage of your good hands that are premium draws is going to be a lot higher. Finally, your odds of being pat (that is, not needing to draw at all) are way higher, about 7% for a pat Nine or better, as opposed to only 2% with five cards.
However, you’re still going to be left without the coveted Seven-Deuce combo 86% of the time. What do your hands look like then? Well, the good news is that you’ll almost always (over 80% of the time) have either the Seven or the Deuce, usually with at least one other low card. In most of these cases, assuming you’re facing only a single raise, you’ll have the odds to call and take one draw to try to improve, and the nice thing about Triple Draw is that the worse your hand is, the easier it is to improve; a three-card draw will almost inevitably improve to a two- or one-card draw, whereas it’s comparatively hard for a one-card draw to complete its hand.
You’re not always going to be happy calling that extra bet, however. If you don’t have the Seven and Deuce, the best thing you can hope to have is a smooth Eight draw. Here, too, having the sixth card produces a marked improvement in your odds; your chances of getting 83xxx or 82xxx (not including 872xx, which we’re counting as a 72xxx) are 20%, as opposed to only 15% with five cards. Overall, then, your total odds of getting dealt a hand that you’re either profitable or at worst not very unprofitable playing under the gun improve from 25% to 34% with the extra card.
|5 Cards||6 Cards|
This isn’t the end of the story, however; there are a couple of other, harder-to-quantify benefits to be had. The first comes from the act of straddling itself, which is that it conceals the strength of your hand those times that you do get dealt something nice. Of course, the other players know that you have six cards, so they know to expect a somewhat stronger hand from you than from someone calling in the big blind in a normal game of 2-7. However, you’re still going to have a hand you would have probably chosen to fold about two-third of the time, so your opponents will have to put you on a considerably wider range than your normal under-the-gun opening range. Assuming you leverage this informational advantage well, your good hands should be more profitable than they are ordinarily, which will somewhat offset the losses you’ll incur by playing the hands which would not have been profitable to open with.
The second is that the added card improves your potential for snowing in the same way it improves your chances of getting dealt a real hand. Snowing is a bluffing strategy in lowball draw games, in which a player bets and raises with a drawing hand but then refrains from drawing, in order to represent a made hand. Usually this is done with hands which are poor as draws, but which contain many low cards; these act as blockers to the potential for opponents to have good hands or to hit their draws. For instance, a player holding 3-3-3-4-5 might attempt to snow, assuming that his opponents will tend to have strong draws (with a 2 and 7) but be unlikely to hit them because so many of their outs are in his hand; assuming they miss and are willing to believe him for even a marginal pat hand, they are likely to call all the way and then fold on the final street, allowing him to buy a large pot with a hand that would have been very weak if played as a draw.
Having the sixth card is a twofold help in snowing. Firstly, it approximately quadruples the odds that the player actually has a pat hand, so it allows him to snow more frequently without losing credibility. Secondly, the potential to hold one extra blocker is important. Six blockers rather than five – or five rather than four, etc. – might not seem that huge of a difference, but you have to turn things around and look at things from the opponent’s perspective; a player drawing a single card is typically looking for two specific cards, so eight outs. Especially in a multiway pot, where opponents are likely to be holding some of one another’s outs too, a theoretical maximum of six blockers can mean that everyone else is drawing very thin indeed.
The most obvious downside to straddling is simply that the player is putting in two bets without even seeing her cards. It’s tempting to call these bets the cost of taking the extra card, but this would be a significant overestimate. First of all, we’ve already said that having six cards means that the player will have a hand where it is at least not very bad to be putting in those two bets something like a third of the time. Thus, the real downside is at most 1.3 big blinds (two-thirds of the two being put in). However, this is also an overestimate, as we’ve said that, most of the time, the player will have a hand with which it is at least worth calling one additional raise and taking a draw; if that call is typically profitable, then it also serves to mitigate the cost of the straddle. For instance, if the button raises, the blinds both fold, and we decide that our call is +1 BB expectation value due to the dead money in the pot, then our net loss from the decision to straddle is actually only 1 BB, not 2 BB.
This is a double-edged sword, however, because it makes one’s reverse implied odds quite nasty. If you don’t want to be giving up too readily when you’ve taken the extra card, then you’re going to be playing at an equity disadvantage a lot of the time, and will be forced to choose between loose calls or tight folds in pretty marginal spots. Perhaps you decide to peel with 52xxx and pick up 86 on the first draw, giving you a single-card draw to a bad Eight High. There’s so much money in the pot already that you probably have to continue, but at the same time, you’re drawing to a hand that might still not win even if you hit. Worse, assuming that someone other than the blinds is in the pot (which is always going to be quite likely given that you straddled blind), you’re going to be out of position, which seriously impedes your ability to avoid mitigate the risk. A call might be profitable in theory (that is, from the standpoint of unexploitable play), yet loss-making in practice if it leads to situations where it’s easy to make costly errors.
The table size issue
What’s important to realize about the downsides is that they depend heavily on the number of players in the game. In the extreme case that you’re playing with only three people, “under the gun” is actually the button, and therefore the best position at the table. You’d often be raising there with a wide variety of hands anyway, and having the extra card advantage only makes it easier to steal the blinds. It’s such a slam-dunk decision in that case that I’d be surprised if anyone actually offered the option in a three-handed game.
Four-handed, it’s still probably a very good move to take the extra card, as Negreanu says. You’re no longer in the best position, but you still have a positional advantage on two of your three opponents. Yes, you will often get raised by the button, and be obliged to call and play out of position with whatever you’re dealt, but if one or both blinds call, you’ll have what we call “relative position” : that is, if you assume that the Button is going to bet when checked to, you will end up being last to act and be able to see how the other players respond to his bet before making your own move. Meanwhile, if they fold, you’ll be heads up with a fairly significant amount of dead money in the pot.
Once we get to five-handed play and beyond, however, it’s less clear cut. If the cutoff raises and the button caps, it’s no longer very easy for you to call if you haven’t been dealt a good hand, so you will in fact find yourself giving up your straddle a lot of the time. You’re also no longer guaranteed to either have the pot heads up, or in a good position.
Furthermore, the more players there are, the higher the requirements are for a reasonable starting hand. The aggression required of four-handed play means that a lot of marginal pat hands, three-card draws and so forth will be in your range to begin with, and you’ll get these quite often when you have the extra card. Conversely, with six or more players, your opening range under the gun should be very tight in triple draw, so even with six cards, you’ll usually find yourself with something you would have preferred to fold ordinarily.
Still, there are enough intangibles in the form of the informational difference and how your opponents adjust their styles that it’s very hard to evaluate either the benefit or the cost of exercising the Straddle-Six option in a quantifiable and comparable way. Like a lot of things in poker, it’s considerably more complex than it appears on the surface, and anyone whose initial gut reaction is that it’s clear cut what the right decision is for medium-sized tables of five or six players has probably not spent enough time thinking about it.
This is the whole point, though; these twists are introduced precisely for the reason that they’re seemingly simple and trick people into making incorrect assumptions. This one is particularly nice in that even when it is profitable from a game theory standpoint, it is going to lead one into situations where the profitable move is not readily identified. Thus, it should produce situations which are profitable for a professional to take, but which end up being a losing proposition for the worse players who seek to emulate them or, even if they are slightly loss-making for the professional, are more so for the amateur. Adding this to the basic fact that it will inevitably make pots larger and bring more players into them (assuming anyone exercises the option at all), it’s pretty clearly in the pros’ advantage to have this rule in play, regardless of whether they plan on taking the extra card themselves or not.
Alex Weldon (@benefactumgames) is a freelance writer, game designer and semipro poker player from Montreal, Quebec, Canada.